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A193932 E.g.f. A(x) = exp(x+x^2+x^3+x^4+x^5+x^6). 2
1, 1, 3, 13, 73, 501, 4051, 32593, 313713, 3326473, 38377891, 476464341, 6299024953, 87715975933, 1314012177843, 20776583119321, 345267365639521, 6009277853650833, 109262845394221123, 2073062512187103133, 41084832105634595241, 845645768972241105541 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..485

FORMULA

a(n)=n!*sum(k=1..n, sum(i=0..(n-k)/6, (-1)^i*binomial(k,k-i)*binomial(n-6*i-1,k-1))/k!), n>0, a(0)=1.

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, add(

      a(n-j)*binomial(n-1, j-1)*j!, j=1..min(n, 6)))

    end:

seq(a(n), n=0..23);  # Alois P. Heinz, Sep 29 2017

MATHEMATICA

With[{nn=20}, CoefficientList[Series[Exp[Total[x^Range[6]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 12 2015 *)

PROG

(Maxima)

a(n):=if n=0 then 1 else n!*sum(sum((-1)^i*binomial(k, k-i)*binomial(n-6*i-1, k-1), i, 0, (n-k)/6)/k!, k, 1, n);

CROSSREFS

Sequence in context: A293196 A193931 A293197 * A193933 A306623 A306624

Adjacent sequences:  A193929 A193930 A193931 * A193933 A193934 A193935

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Aug 09 2011

STATUS

approved

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Last modified October 21 13:15 EDT 2021. Contains 348155 sequences. (Running on oeis4.)